In the past, there have been known SOx concentration sensors for detecting the SOx concentration in the exhaust gas. These known SOx concentration sensors normally use solid electrolytes and measure the electromotive force generated by the change of SOx into sulfate ions to detect the SOx concentration in the exhaust gas (for example, see Japanese Patent Publication (A) No. 2004-239706).
However, a conventional SOx detection system using this kind of SOx concentration sensor can only operate under high temperatures and becomes bulky as an apparatus. In particular, when the SOx concentration is low, there is the large problem of not being able to detect the SOx concentration. Conventionally, as in this SOx concentration sensor, attention has only been directed at instantaneously detecting the SOx concentration. So long as trying to instantaneously detect the SOx concentration in such a way, various problems inevitably occur like as explained above.
Therefore, the inventors changed their way of thinking and focused not on instantaneously detecting the SOx concentration, but on detecting the cumulative amount of sulfur SOx released over a long period. Further, by changing their thinking in this way, it became possible to easily detect the cumulative amount of the SOx exhausted over a long period of time and possible to estimate the amount of SOx stored in the catalyst arranged in the engine exhaust passage from this cumulative amount of the SOx.
However, it was learned that, when estimating the amount of SOx stored in the catalyst from the cumulative amount of the SOx, if not considering the SOx trapping rate when detecting the cumulative amount of the SOx and the SOx trapping rate of the catalyst, the estimated value of the stored amount of SOx ended up deviating from the normal value.